Hypercontractive Measures, Talagrand’s Inequality, and Influences

  • Dario Cordero-ErausquinEmail author
  • Michel Ledoux
Part of the Lecture Notes in Mathematics book series (LNM, volume 2050)


We survey several Talagrand type inequalities and their application to influences with the tool of hypercontractivity for both discrete and continuous, and product and non-product models. The approach covers similarly by a simple interpolation the framework of geometric influences recently developed by N. Keller, E. Mossel and A. Sen. Geometric Brascamp-Lieb decompositions are also considered in this context.


Cayley Graph Dirichlet Form Logarithmic Sobolev Inequality Markov Operator Markov Semigroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank F. Barthe and P. Cattiaux for their help with the bound (26), and R. Rossignol for pointing out to us the references [20, 21]. We also thank J. van den Berg and D. Kiss for pointing out that the techniques developed here cover the example of the complete graph and for letting us know about [14].


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institut de MathématiquesUniversité Pierre et Marie Curie (Paris 6 – Jussieu)ParisFrance
  2. 2.Institut Universitaire de FranceParisFrance
  3. 3.Institut de Mathématiques de ToulouseUniversité de ToulouseToulouseFrance

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